Block #379,718

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 5:29:51 PM · Difficulty 10.4193 · 6,445,940 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

38b28ea164647c8376b43bf6c1f192311f590fdcf92fe8fd0c24ce094c349b23

View on Chainz ↗

Height

#379,718

Difficulty

10.419262

Transactions

Size

208 B

Version

Bits

0a6b54c2

Nonce

18,507

Timestamp

1/28/2014, 5:29:51 PM

Confirmations

6,445,940

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

eefe80dffca6a89e6b0bc710653b5a56c193baab0328db286fc0ebf2455c2c3d

Transactions (1)

Coinbaseeefe80dffca6a8…c0ebf2455c2c3d

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.107 × 10⁹⁸(99-digit number)

51071988211477911417…57027674831704079679

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

5.107 × 10⁹⁸(99-digit number)

51071988211477911417…57027674831704079679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.107 × 10⁹⁸(99-digit number)

51071988211477911417…57027674831704079681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.021 × 10⁹⁹(100-digit number)

10214397642295582283…14055349663408159359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.021 × 10⁹⁹(100-digit number)

10214397642295582283…14055349663408159361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.042 × 10⁹⁹(100-digit number)

20428795284591164567…28110699326816318719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.042 × 10⁹⁹(100-digit number)

20428795284591164567…28110699326816318721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.085 × 10⁹⁹(100-digit number)

40857590569182329134…56221398653632637439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.085 × 10⁹⁹(100-digit number)

40857590569182329134…56221398653632637441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

8.171 × 10⁹⁹(100-digit number)

81715181138364658268…12442797307265274879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.171 × 10⁹⁹(100-digit number)

81715181138364658268…12442797307265274881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #379,718

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